Bring a pot of lightly salted water to a boil for the pasta.
Mix the tomato paste, balsamic vinegar, garlic, Italian seasoning, and water together. Set aside.
Heat the olive oil in a large pan over medium-high heat. Once hot, add the onion and peppers. Toss to evenly coat in the oil and season with a pinch of salt and pepper. Cook for 5-6 minutes until the veggies start to soften and brown in spots. Transfer to a bowl and set aside.
Start cooking the pasta at this step. Cook until just shy of al dente (1-2 minutes shorter than the recommended cook time on the pasta’s packaging.)
Add the beef to the same pan and cook for 2-3 minutes on one side until nicely browned. Use a spatula to break the beef apart and fully cook.
Add the mixed sauce to the cooked beef, stirring until evenly incorporated. Fold in the basil with the beef and cook until wilted, another 1-2 minutes.
Toss the veggies with the beef and keep warm until the pasta is ready.
Reserve about 1 cup of the pasta water before draining the rest. Add the cooked pasta and parmesan to the beef and peppers. Fold everything together, adding a couple tablespoons of the reserved pasta water at a time, until a smooth sauce forms. (I used about 2/3 cup of pasta water.)
Salt to taste before serving. Garnish with extra grated parmesan, black pepper, and a drizzle of olive oil, if desired.